Translation:Do not look!
There isn't a difference in meaning between the two, when used as a command meaning "don't". I've seen some people claim that one is more formal than the other, but it doesn't seem like people even agree which one is more formal. For all practical purposes, they're interchangeable.
The main difference is that 不要 can also be used to mean "don't want", whereas 别 doesn't have this alternate meaning. E.g. 我不要这本书 means "I don't want this book", but replacing 不要 with 别 produces a nonsensical sentence.
别 means alternate. 不要 means don't want. So, 别看 means, "Look elsewhere!" 不要看 means, "I don't want you to look." They both effectively mean the same thing. However, if you want to say, "someone else," you would say 别人. 不要人 would mean, "I don't want any human."